Written Assignment 9
Answer all assigned exercises, and show all work. Submit your
work to the mentor by Sunday of Week 10. 1. Changes in population—Many factors may contribute to population
changes in metropolitan areas. The graph shows the populations of
the New Orleans, Louisiana and the Jacksonville, Florida,
metropolitan areas over the years 2004–2009. Use the terms increasing, decreasing, and constant to describe the
trends for the population of the New Orleans metropolitan area. [4
points]
Trends for the population of the New Orleans metropolitan area so that
population is decreasing. 2. Solve the system by substitution. (See section 5.1, Example 1.) [4
points]
4x 5 y 7 (1)
9 y 31 2x (2) 3. Solve the system by elimination. (See section 5.1, Example 2.) [4
points] 12x 5 y 9
3x 8 y 18 4. Solve each system. State whether it is inconsistent or has infinitely
many solutions. If the system has infinitely many solutions, write the
solution set with y arbitrary. (See section 5.1, Examples 3and 4.) [8
points]
3x 2 y 5 a. 6x 4 y 8 3x 5 y 2 b. 9x 15 y 6 5. Solve the system. (See section 5.1, Example 6.) [4 points]
4x 3y z 9
3x 2 y 2z 4
x y 3z 5 6. Solve the system. State whether it is inconsistent or has infinitely
many solutions. If the system has infinitely many solutions, write the
solution set with y arbitrary. (See section 5.1, Examples 3, 4, 6, and
7.) [4 points]
3x y 3z 1
x2y z2
2x y 4z 4 7. Solve the system. (Hint: let
2
x
4 3
y
5 18 8 1
x t and 1
y u .) [4 points] x y 8. Use a system to find the equation of the parabola through the given
points. [4 points] 9. Investment decisions—Jane Hooker invests $40,000 received as an
inheritance in three parts. With one part she buys mutual funds that
offer a return of 2% per year. The second part, which amounts to
twice the first, is used to buy government bonds paying 2.5% per
year. She puts the rest of the money into a savings account that pays
1.25% annual interest. During the first year, the total interest is $825.
How much did she invest at each rate? (See section 5.1, Examples 5
and 9) [4 points] 10. Give all solutions of each nonlinear system of equations, including
those nonreal complex components. [24 points]
2 a. x y2
xy0 2 b. 2 x y 10
2 2 c. 2 2x y 17 2 x y 4
2 2 5x 5 y 28 d. 5xy 2 0
x 15y 5 2 e. f. 2 x 3xy y 12
2 2 2 2 x y 12 x y 9
x y 11. Unknown numbers—Using a system of equations in two variables,
find two numbers whose sum is 10 and whose squares differ by 20.
(See section 5.5, Example 6.) [4 points] 12. (Modeling) Circuit gain—In electronics, circuit gain is modeled by
G Bt , R Rt where R is the value of a resistor, t is the temperature, Rt is the value
of R at temperature t, and B is a constant. The sensitivity of the circuit
to temperature is modeled by
S BR .
R Rt 2 If B = 3.7 and t is 90 K (kelvins), use a system of equations in two
variables to find the values of R and Rt that will result in the values of
G = 0.4 and S = 0.001. [4 points] 13. Graph each horizontal parabola, and give the domain and range.
(See section 6.1, Examples 1 and 2.) [12 points] a. x2y 2 b. x 4 1
2 ( y 1) 2 2 c. x 2y 2y 3 14. Give the focus, directrix, and axis of symmetry for each parabola.
(See section 6.1, Example 3.) [8 points]
a. 2 x 1
8 y b. x 16 y 2 15. Write an equation for each parabola with vertex at the origin.
(See section 6.1, Example 4.) [8 points]
a. b. through 2, 2 2 , opening left c. through 2, 4 , symmetric with respect to the y-axis